Flux out of a Cylindrical Cable

AI Thread Summary
The discussion revolves around calculating the electric field in a coaxial transmission line with inner and outer conducting cylinders, focusing on different regions defined by their radii. For r<a, the electric field is zero due to no enclosed charge. The user seeks clarification on determining the components of the vector dS in the region a<r<b, expressing confusion about visualizing this concept. Resources are shared to help understand cylindrical coordinates and surface elements without needing to memorize them. The emphasis is on grasping the underlying principles rather than rote memorization.
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Homework Statement



A coaxial transmission line has an inner conducting cylinder of radius a and an outer conducting cylinder of radius c. Charge ql per unit length is uniformly distributed over the inner conductor and -ql over the outer. If dielectric \epsilon_{1} extends from r=a to r=b and dielectric \epsilon_{2} from r=b r=c, find the electric field for r<a, for a<r<b, for b<r<c and for r>c. Take the conducting cylinders as infinitesimally thin.

Homework Equations





The Attempt at a Solution



For r<a there is no charge enclosed thus the flux is 0 so E is also 0

Here is the solution they give for a<r<b. (see figure attached)

I am confused as to how he determines the components of the vector d\vec{S}. Is there a picture that will explain this?

Thanks again!
 

Attachments

  • Sol1.4a.JPG
    Sol1.4a.JPG
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quietrain said:
http://hyperphysics.phy-astr.gsu.edu/hbase/sphc.html
scroll down to cylindrical polar coordinates

http://en.wikipedia.org/wiki/Cylindrical_coordinate_system#Line and volume elements
scroll down to line and volume elements section, of surface element

that is how he got the ds which is the surface element of cylinder in cylindrical coordinates.

i can't help you on the rest, because i forgot my electromag already ::(

The wiki gives me the line, surface and volume elements but I don't want to have to memorize them.

Isn't there a more intuitive way of understanding this as opposed to memorizing it?
 
you are not suppose to memorize them, they should be given in the exams.

you are suppose to understand how to get them

take a look at these for more info

http://www.math.ubc.ca/~feldman/m227/coordsys.pdf

http://www.math.montana.edu/frankw/ccp/multiworld/multipleIVP/cylindrical/learn.htm
 
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